Volume 49, Issue 2
Kuramoto-Sivashinsky Equation and Free-interface Models in Combustion Theory

Claude-Michel Brauner

10.4208/jms.v49n2.16.01

J. Math. Study, 49 (2016), pp. 93-110.

Full Article 4 60
  • Abstract

In combustion theory, a thin flame zone is usually replaced by a free interface. A very challenging problem is the derivation of a self-consistent equation for the flame front which yields a reduction of the dimensionality of the system. A paradigm is the Kuramoto-Sivashinsky (K-S) equation, which models cellular instabilities and turbulence phenomena. In this survey paper, we browse through a series of models in which one reaches a fully nonlinear parabolic equation for the free interface, involving pseudo-differential operators. The K-S equation appears to be asymptotically the lowest order of approximation near the threshold of stability.

  • History

Submitted: 2016-07

Accepted: 2019-03

Published online: 2016-07

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